Solve sqrt{1-(0.1446/104.2343)}=

$$\sqrt { 1 - ( 0.1446 / 104.2343 ) } =$$

Evaluate

$$\frac{\sqrt{67577978143}}{260000}\approx 0.999837103$$

Solution Steps

Expand \frac{0.1446}{104} by multiplying both numerator and the denominator by 10000.

$$\sqrt{1-\frac{1446}{1040000}\times 0.2343}$$

Reduce the fraction \frac{1446}{1040000} to lowest terms by extracting and canceling out 2.

$$\sqrt{1-\frac{723}{520000}\times 0.2343}$$

Convert decimal number 0.2343 to fraction \frac{2343}{10000}.

$$\sqrt{1-\frac{723}{520000}\times \frac{2343}{10000}}$$

Multiply \frac{723}{520000} times \frac{2343}{10000} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{1-\frac{723\times 2343}{520000\times 10000}}$$

Do the multiplications in the fraction \frac{723\times 2343}{520000\times 10000}.

$$\sqrt{1-\frac{1693989}{5200000000}}$$

Convert 1 to fraction \frac{5200000000}{5200000000}.

$$\sqrt{\frac{5200000000}{5200000000}-\frac{1693989}{5200000000}}$$

Since \frac{5200000000}{5200000000} and \frac{1693989}{5200000000} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{5200000000-1693989}{5200000000}}$$

Subtract 1693989 from 5200000000 to get 5198306011.

$$\sqrt{\frac{5198306011}{5200000000}}$$

Rewrite the square root of the division \sqrt{\frac{5198306011}{5200000000}} as the division of square roots \frac{\sqrt{5198306011}}{\sqrt{5200000000}}.

$$\frac{\sqrt{5198306011}}{\sqrt{5200000000}}$$

Factor 5200000000=20000^{2}\times 13. Rewrite the square root of the product \sqrt{20000^{2}\times 13} as the product of square roots \sqrt{20000^{2}}\sqrt{13}. Take the square root of 20000^{2}.

$$\frac{\sqrt{5198306011}}{20000\sqrt{13}}$$

Rationalize the denominator of \frac{\sqrt{5198306011}}{20000\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{5198306011}\sqrt{13}}{20000\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{5198306011}\sqrt{13}}{20000\times 13}$$

To multiply \sqrt{5198306011} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\sqrt{67577978143}}{20000\times 13}$$

Multiply 20000 and 13 to get 260000.

$$\frac{\sqrt{67577978143}}{260000}$$